Question

Suppose you've just inherited $10,000 from a relative. You're trying to decide whether to put the $10,000 in a non-interest-bearing checking account so that you can use it whenever you want (that is, hold it as money), or to use it to buy a U.S. Treasury bond. Suppose the interest rate on the bond is 5% per year.

a) What would be the opportunity cost of holding the $10,000 as money?
b) Suppose the interest rate fell to 2% per year. What would happen to the opportunity cost of holding the $10,000 as money?
c) What does this previous analysis suggest about the market for money?

Answer 1

a) What would be the opportunity cost of holding the $10,000 as money?

To find the answer, we use the future value of an investment formula to find the value of the investment in the treasury bond.

FV = PV (1 +i)^n

Where:

• FV = future value
• PV = present value
• i = interest rate
• n = number of compounding periods

Now, we simply replace the values into the formula:

FV = 10,000 (1 + 0.05)^1

FV = 10,500

The opportunity cost is the $500 in interest that you would receive if you bought the treasury bond.

b) Suppose the interest rate fell to 2% per year. What would happen to the opportunity cost of holding the $10,000 as money?

We use the same formula to find the answer:

FV = 10,000 (1 + 0.02)^1

FV = 10,200

The new opportunity cost is $200, so the opportunity cost would fall by $300.

c) What does this previous analysis suggest about the market for money?

Because money loses value in time due to inflation, it's always best to save the cash in an interest-bearing account, because the interest earned offsets the lose of value.